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SMO 2017 Open Round 1 Question 18

SMO · SMO 2017 Open Round 1

Question 18

Let $f(x)=\sqrt{x^2-10x+314}+\sqrt{x^2+20x+325}$. Find the minimum value of $[f(x)]$ for real number $x$.

Source notation: $[t]$ denotes the greatest integer less than or equal to $t$.